18 Search Results for "Clairambault, Pierre"

Document
DOI: 10.4230/LIPIcs.CSL.2026.12
String Diagrams for Closed Symmetric Monoidal Categories

Authors: Callum Reader and Alessandro Di Giorgio

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor explicit, allowing standard morphism wires to interact with them through a well-defined set of graphical rules. We establish the soundness and completeness of the diagrammatic calculus, and illustrate its expressiveness through examples drawn from category theory, logic and programming language semantics.
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Callum Reader and Alessandro Di Giorgio. String Diagrams for Closed Symmetric Monoidal Categories. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{reader_et_al:LIPIcs.CSL.2026.12,
  author =	{Reader, Callum and Di Giorgio, Alessandro},
  title =	{{String Diagrams for Closed Symmetric Monoidal Categories}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{12:1--12:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.12},
  URN =		{urn:nbn:de:0030-drops-254369},
  doi =		{10.4230/LIPIcs.CSL.2026.12},
  annote =	{Keywords: diagrammatic languages, logic, lambda calculi}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.40
The Groupoid-Syntax of Type Theory Is a Set

Authors: Thorsten Altenkirch, Ambrus Kaposi, and Szumi Xie

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Categories with families (CwFs) have been used to define the semantics of type theory in type theory. In the setting of Homotopy Type Theory (HoTT), one of the limitations of the traditional notion of CwFs is the requirement to set-truncate types, which excludes models based on univalent categories, such as the standard set model. To address this limitation, we introduce the concept of a Groupoid Category with Families (GCwF). This framework truncates types at the groupoid level and incorporates coherence equations, providing a natural extension of the CwF framework when starting from a 1-category. We demonstrate that the initial GCwF for a type theory with a base family of sets and Π-types (groupoid-syntax) is set-truncated. Consequently, this allows us to utilize the conventional intrinsic syntax of type theory while enabling interpretations in semantically richer and more natural models. All constructions in this paper were formalised in Cubical Agda.
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Thorsten Altenkirch, Ambrus Kaposi, and Szumi Xie. The Groupoid-Syntax of Type Theory Is a Set. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 40:1-40:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{altenkirch_et_al:LIPIcs.CSL.2026.40,
  author =	{Altenkirch, Thorsten and Kaposi, Ambrus and Xie, Szumi},
  title =	{{The Groupoid-Syntax of Type Theory Is a Set}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{40:1--40:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.40},
  URN =		{urn:nbn:de:0030-drops-254650},
  doi =		{10.4230/LIPIcs.CSL.2026.40},
  annote =	{Keywords: Categorical models of type theory, category with families, groupoids, coherence, homotopy type theory}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CSL.2026.4
Towards A Rosetta Stone of Interactive and Quantitative Semantics (Invited Talk)

Authors: Pierre Clairambault

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Quantitative semantics are those denotational semantics that inherit from linear logic [Jean-Yves Girard, 1987] a sensitivity to the multiplicity of resources involved in computation. Those include the relational model [Jean-Yves Girard, 1987] and its numerous variations (such as finiteness spaces [Thomas Ehrhard, 2005], weighted relational models [Jim Laird et al., 2013] and their extensions [Thomas Ehrhard et al., 2011; Thomas Ehrhard, 2002], generalized species of structure [Fiore et al., 2008], span models [Paul-André Melliès, 2019; Pierre Clairambault and Simon Forest, 2023], etc), as well as related syntactic methods such as non-idempotent intersection types [Daniel de Carvalho, 2018] and Taylor expansion of lambda-terms [Thomas Ehrhard and Laurent Regnier, 2003]. Interactive semantics are usually also quantitative, but in addition they present the interactive behaviour of proofs and programs, generally organized chronologically - those include the many variants of game semantics (starting with [J. M. E. Hyland and C.-H. Luke Ong, 2000; Samson Abramsky et al., 2000]), and other frameworks such as Geometry of Interaction [Girard, 1989] or ludics [Jean-Yves Girard, 2001]. Both families are cornerstones of modern denotational semantics, and both have associated Alonzo Church awards: game semantics in 2017, and quantitative semantics (in particular, differential linear logic and the differential λ-calculus) in 2024. It has more or less always been clear to the experts that the two, sharing an origin in linear logic, are conceptually related. Yet there are differences, which seem fundamental: in particular, while quantitative models compose relationally, the composition of strategies follows an intricate "parallel interaction plus hiding" process inspired from concurrency theory [Abramsky, 1997]. The two families of models have also historically targeted different kinds of languages: whereas quantitative semantics focused on theoretical calculi (and the λ-calculus in particular), game semantics is known for fully abstract models for languages with elaborate combinations of effects including local state [Samson Abramsky and Guy McCusker, 1996], control operators [James Laird, 1997], and concurrent primitives [Dan R. Ghica and Andrzej S. Murawski, 2008]. Early on, researchers have explored the relationship between the two [Thomas Ehrhard, 1996; Patrick Baillot et al., 1997], and investigations on this question have spanned decades [Pierre Boudes, 2009; Ana C. Calderon and Guy McCusker, 2010; Takeshi Tsukada and C.-H. Luke Ong, 2016; C.-H. Luke Ong, 2017]. In particular, Melliès' work on asynchronous games [Paul-André Melliès, 2006; Paul-André Melliès, 2005] made significant conceptual contributions, showing that the issue was enlightened by adopting a positional formulation of game semantics, where points in the relational model simply arise as certain positions. This talk surveys recent developments in this line of work, shedding light on the connection between those two families. Our work is set in so-called "thin concurrent games" [Simon Castellan et al., 2019; Pierre Clairambault, 2024], an extension with symmetry of Rideau and Winskel’s concurrent games on event structures [Silvain Rideau and Glynn Winskel, 2011]. Event structures being one of the main "truly concurrent" models of concurrency [Glynn Winskel, 1986], it is perhaps expected that thin concurrent games can model concurrent languages: they provide a truly concurrent refinement of Ghica and Murawski’s fully abstract model of Idealized Concurrent Algol [Simon Castellan and Pierre Clairambault, 2024; Pierre Clairambault, 2024]. But beyond the semantics of concurrency, thin concurrent games are also a deep reworking on game semantics built from causal principles, inheriting from asynchronous games a positional flavour. In thin concurrent games, strategies have a dual nature: an event-based nature where they appear as certain event structures composed via parallel interaction plus hiding; or a positional nature where they appear as certain spans of groupoids, composed by pullback (modulo a technical condition on strategies called visibility) - they can be regarded both as a games and a relational model! Leveraging this dual nature, in a sequence of papers with Castellan, de Visme, Olimpieri and Paquet, we have been able to link the single framework of thin concurrent games with numerous other models. This includes various traditional alternating or non-alternating games models [Simon Castellan and Pierre Clairambault, 2024; Pierre Clairambault, 2024], the weighted relational model [Pierre Clairambault and Hugo Paquet, 2021], the quantum relational model [Pierre Clairambault and Marc de Visme, 2020], generalized species of structure [Pierre Clairambault et al., 2023], and - going beyond quantitative semantics - the linear Scott model [Clairambault, 2025], a linear decomposition of standard Scott domain semantics [Thomas Ehrhard, 2012]. All these distinct models are obtained by projecting away certain aspects of thin concurrent games, giving some support to the claim that thin concurrent games are a Rosetta stone for interactive and quantitative semantics.
Cite as

Pierre Clairambault. Towards A Rosetta Stone of Interactive and Quantitative Semantics (Invited Talk). In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 4:1-4:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{clairambault:LIPIcs.CSL.2026.4,
  author =	{Clairambault, Pierre},
  title =	{{Towards A Rosetta Stone of Interactive and Quantitative Semantics}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{4:1--4:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.4},
  URN =		{urn:nbn:de:0030-drops-254286},
  doi =		{10.4230/LIPIcs.CSL.2026.4},
  annote =	{Keywords: Denotational semantics, Game semantics}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.68
Slightly Non-Linear Higher-Order Tree Transducers

Authors: Lê Thành Dũng (Tito) Nguyễn and Gabriele Vanoni

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We investigate the tree-to-tree functions computed by "affine λ-transducers": tree automata whose memory consists of an affine λ-term instead of a finite state. They can be seen as variations on Gallot, Lemay and Salvati’s Linear High-Order Deterministic Tree Transducers. When the memory is almost purely affine (à la Kanazawa), we show that these machines can be translated to tree-walking transducers (and with a purely affine memory, we get a reversible tree-walking transducer). This leads to a proof of an inexpressivity conjecture of Nguyễn and Pradic on "implicit automata" in an affine λ-calculus. We also prove that a more powerful variant, extended with preprocessing by an MSO relabeling and allowing a limited amount of non-linearity, is equivalent in expressive power to Engelfriet, Hoogeboom and Samwel’s invisible pebble tree transducers. The key technical tool in our proofs is the Interaction Abstract Machine (IAM), an operational avatar of Girard’s geometry of interaction, a semantics of linear logic. We work with ad-hoc specializations to λ-terms of low exponential depth of a tree-generating version of the IAM.
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Lê Thành Dũng (Tito) Nguyễn and Gabriele Vanoni. Slightly Non-Linear Higher-Order Tree Transducers. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 68:1-68:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nguyen_et_al:LIPIcs.STACS.2025.68,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng (Tito) and Vanoni, Gabriele},
  title =	{{Slightly Non-Linear Higher-Order Tree Transducers}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{68:1--68:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.68},
  URN =		{urn:nbn:de:0030-drops-228934},
  doi =		{10.4230/LIPIcs.STACS.2025.68},
  annote =	{Keywords: Almost affine lambda-calculus, geometry of interaction, reversibility, tree transducers, tree-walking automata}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.23
How to Play the Accordion: Uniformity and the (Non-)Conservativity of the Linear Approximation of the λ-Calculus

Authors: Rémy Cerda and Lionel Vaux Auclair

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Twenty years after its introduction by Ehrhard and Regnier, differentiation in λ-calculus and in linear logic is now a celebrated tool. In particular, it allows to write the Taylor formula in various λ-calculi, hence providing a theory of linear approximations for these calculi. In the standard λ-calculus, this linear approximation is expressed by results stating that the (possibly) infinitary β-reduction of λ-terms is simulated by the reduction of their Taylor expansion: in terms of rewriting systems, the resource reduction (operating on Taylor approximants) is an extension of the β-reduction. In this paper, we address the converse property, conservativity: are there reductions of the Taylor approximants that do not arise from an actual β-reduction of the approximated term? We show that if we restrict the setting to finite terms and β-reduction sequences, then the linear approximation is conservative. However, as soon as one allows infinitary reduction sequences this property is broken. We design a counter-example, the Accordion. Then we show how restricting the reduction of the Taylor approximants allows to build a conservative extension of the β-reduction preserving good simulation properties. This restriction relies on uniformity, a property that was already at the core of Ehrhard and Regnier’s pioneering work.
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Rémy Cerda and Lionel Vaux Auclair. How to Play the Accordion: Uniformity and the (Non-)Conservativity of the Linear Approximation of the λ-Calculus. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cerda_et_al:LIPIcs.STACS.2025.23,
  author =	{Cerda, R\'{e}my and Vaux Auclair, Lionel},
  title =	{{How to Play the Accordion: Uniformity and the (Non-)Conservativity of the Linear Approximation of the \lambda-Calculus}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{23:1--23:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.23},
  URN =		{urn:nbn:de:0030-drops-228480},
  doi =		{10.4230/LIPIcs.STACS.2025.23},
  annote =	{Keywords: program approximation, quantitative semantics, lambda-calculus, linear approximation, Taylor expansion, conservativity}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2023.13
Strategies as Resource Terms, and Their Categorical Semantics

Authors: Lison Blondeau-Patissier, Pierre Clairambault, and Lionel Vaux Auclair

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
As shown by Tsukada and Ong, simply-typed, normal and η-long resource terms correspond to plays in Hyland-Ong games, quotiented by Melliès' homotopy equivalence. Though inspiring, their proof is indirect, relying on the injectivity of the relational model {w.r.t.} both sides of the correspondence - in particular, the dynamics of the resource calculus is taken into account only via the compatibility of the relational model with the composition of normal terms defined by normalization. In the present paper, we revisit and extend these results. Our first contribution is to restate the correspondence by considering causal structures we call augmentations, which are canonical representatives of Hyland-Ong plays up to homotopy. This allows us to give a direct and explicit account of the connection with normal resource terms. As a second contribution, we extend this account to the reduction of resource terms: building on a notion of strategies as weighted sums of augmentations, we provide a denotational model of the resource calculus, invariant under reduction. A key step - and our third contribution - is a categorical model we call a resource category, which is to the resource calculus what differential categories are to the differential λ-calculus.
Cite as

Lison Blondeau-Patissier, Pierre Clairambault, and Lionel Vaux Auclair. Strategies as Resource Terms, and Their Categorical Semantics. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{blondeaupatissier_et_al:LIPIcs.FSCD.2023.13,
  author =	{Blondeau-Patissier, Lison and Clairambault, Pierre and Vaux Auclair, Lionel},
  title =	{{Strategies as Resource Terms, and Their Categorical Semantics}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{13:1--13:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.13},
  URN =		{urn:nbn:de:0030-drops-179976},
  doi =		{10.4230/LIPIcs.FSCD.2023.13},
  annote =	{Keywords: Resource calculus, Game semantics, Categorical semantics}
}
Document
DOI: 10.4230/LIPIcs.CSL.2023.10
The Functional Machine Calculus II: Semantics

Authors: Chris Barrett, Willem Heijltjes, and Guy McCusker

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
The Functional Machine Calculus (FMC), recently introduced by the second author, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input. Significantly, it remains confluent and can be simply typed in the presence of these effects. In this paper, we explore the denotational semantics of the FMC. We have three main contributions: first, we argue that its syntax - in which both effects and lambda-calculus are realised using the same syntactic constructs - is semantically natural, corresponding closely to the structure of a Scott-style domain theoretic semantics. Second, we show that simple types confer strong normalization by extending Gandy’s proof for the lambda-calculus, including a small simplification of the technique. Finally, we show that the typed FMC (without considering the specifics of encoded effects), modulo an appropriate equational theory, is a complete language for Cartesian closed categories.
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Chris Barrett, Willem Heijltjes, and Guy McCusker. The Functional Machine Calculus II: Semantics. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{barrett_et_al:LIPIcs.CSL.2023.10,
  author =	{Barrett, Chris and Heijltjes, Willem and McCusker, Guy},
  title =	{{The Functional Machine Calculus II: Semantics}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.10},
  URN =		{urn:nbn:de:0030-drops-174716},
  doi =		{10.4230/LIPIcs.CSL.2023.10},
  annote =	{Keywords: lambda-calculus, computational effects, denotational semantics, strong normalization}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.17
Positional Injectivity for Innocent Strategies

Authors: Lison Blondeau-Patissier and Pierre Clairambault

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
In asynchronous games, Melliès proved that innocent strategies are positional: their behaviour only depends on the position, not the temporal order used to reach it. This insightful result shaped our understanding of the link between dynamic (i.e. game) and static (i.e. relational) semantics. In this paper, we investigate the positionality of innocent strategies in the traditional setting of Hyland-Ong-Nickau-Coquand pointer games. We show that though innocent strategies are not positional, total finite innocent strategies still enjoy a key consequence of positionality, namely positional injectivity: they are entirely determined by their positions. Unfortunately, this does not hold in general: we show a counter-example if finiteness and totality are lifted. For finite partial strategies we leave the problem open; we show however the partial result that two strategies with the same positions must have the same P-views of maximal length.
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Lison Blondeau-Patissier and Pierre Clairambault. Positional Injectivity for Innocent Strategies. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 17:1-17:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{blondeaupatissier_et_al:LIPIcs.FSCD.2021.17,
  author =	{Blondeau-Patissier, Lison and Clairambault, Pierre},
  title =	{{Positional Injectivity for Innocent Strategies}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{17:1--17:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.17},
  URN =		{urn:nbn:de:0030-drops-142555},
  doi =		{10.4230/LIPIcs.FSCD.2021.17},
  annote =	{Keywords: Game Semantics, Innocence, Relational Semantics, Positionality}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.135
Implicit Automata in Typed λ-Calculi I: Aperiodicity in a Non-Commutative Logic

Authors: Lê Thành Dũng Nguyễn and Cécilia Pradic

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We give a characterization of star-free languages in a λ-calculus with support for non-commutative affine types (in the sense of linear logic), via the algebraic characterization of the former using aperiodic monoids. When the type system is made commutative, we show that we get regular languages instead. A key ingredient in our approach – that it shares with higher-order model checking – is the use of Church encodings for inputs and outputs. Our result is, to our knowledge, the first use of non-commutativity in implicit computational complexity.
Cite as

Lê Thành Dũng Nguyễn and Cécilia Pradic. Implicit Automata in Typed λ-Calculi I: Aperiodicity in a Non-Commutative Logic. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 135:1-135:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{nguyen_et_al:LIPIcs.ICALP.2020.135,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng and Pradic, C\'{e}cilia},
  title =	{{Implicit Automata in Typed \lambda-Calculi I: Aperiodicity in a Non-Commutative Logic}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{135:1--135:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.135},
  URN =		{urn:nbn:de:0030-drops-125426},
  doi =		{10.4230/LIPIcs.ICALP.2020.135},
  annote =	{Keywords: Church encodings, ordered linear types, star-free languages}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2019.9
Causal Unfoldings

Authors: Marc de Visme and Glynn Winskel

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)

Abstract
In the simplest form of event structure, a prime event structure, an event is associated with a unique causal history, its prime cause. However, it is quite common for an event to have disjunctive causes in that it can be enabled by any one of multiple sets of causes. Sometimes the sets of causes may be mutually exclusive, inconsistent one with another, and sometimes not, in which case they coexist consistently and constitute parallel causes of the event. The established model of general event structures can model parallel causes. On occasion however such a model abstracts too far away from the precise causal histories of events to be directly useful. For example, sometimes one needs to associate probabilities with different, possibly coexisting, causal histories of a common event. Ideally, the causal histories of a general event structure would correspond to the configurations of its causal unfolding to a prime event structure; and the causal unfolding would arise as a right adjoint to the embedding of prime in general event structures. But there is no such adjunction. However, a slight extension of prime event structures remedies this defect and provides a causal unfolding as a universal construction. Prime event structures are extended with an equivalence relation in order to dissociate the two roles, that of an event and its enabling; in effect, prime causes are labelled by a disjunctive event, an equivalence class of its prime causes. With this enrichment a suitable causal unfolding appears as a pseudo right adjoint. The adjunction relies critically on the central and subtle notion of extremal causal realisation as an embodiment of causal history.
Cite as

Marc de Visme and Glynn Winskel. Causal Unfoldings. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{devisme_et_al:LIPIcs.CALCO.2019.9,
  author =	{de Visme, Marc and Winskel, Glynn},
  title =	{{Causal Unfoldings}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.9},
  URN =		{urn:nbn:de:0030-drops-114376},
  doi =		{10.4230/LIPIcs.CALCO.2019.9},
  annote =	{Keywords: Event Structures, Parallel Causes, Causal Unfolding, Probability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.50
On the Expressivity of Linear Recursion Schemes

Authors: Pierre Clairambault and Andrzej S. Murawski

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We investigate the expressive power of higher-order recursion schemes (HORS) restricted to linear types. Two formalisms are considered: multiplicative additive HORS (MAHORS), which feature both linear function types and products, and multiplicative HORS (MHORS), based on linear function types only. For MAHORS, we establish an equi-expressivity result with a variant of tree-stack automata. Consequently, we can show that MAHORS are strictly more expressive than first-order HORS, that they are incomparable with second-order HORS, and that the associated branch languages lie at the third level of the collapsible pushdown hierarchy. In the multiplicative case, we show that MHORS are equivalent to a special kind of pushdown automata. It follows that any MHORS can be translated to an equivalent first-order MHORS in polynomial time. Further, we show that MHORS generate regular trees and can be translated to equivalent order-0 HORS in exponential time. Consequently, MHORS turn out to have the same expressive power as 0-HORS but they can be exponentially more concise. Our results are obtained through a combination of techniques from game semantics, the geometry of interaction and automata theory.
Cite as

Pierre Clairambault and Andrzej S. Murawski. On the Expressivity of Linear Recursion Schemes. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{clairambault_et_al:LIPIcs.MFCS.2019.50,
  author =	{Clairambault, Pierre and Murawski, Andrzej S.},
  title =	{{On the Expressivity of Linear Recursion Schemes}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{50:1--50:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.50},
  URN =		{urn:nbn:de:0030-drops-109945},
  doi =		{10.4230/LIPIcs.MFCS.2019.50},
  annote =	{Keywords: higher-order recursion schemes, linear logic, game semantics, geometry of interaction}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.5
The True Concurrency of Herbrand's Theorem

Authors: Aurore Alcolei, Pierre Clairambault, Martin Hyland, and Glynn Winskel

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Herbrand's theorem, widely regarded as a cornerstone of proof theory, exposes some of the constructive content of classical logic. In its simplest form, it reduces the validity of a first-order purely existential formula to that of a finite disjunction. In the general case, it reduces first-order validity to propositional validity, by understanding the structure of the assignment of first-order terms to existential quantifiers, and the causal dependency between quantifiers. In this paper, we show that Herbrand's theorem in its general form can be elegantly stated and proved as a theorem in the framework of concurrent games, a denotational semantics designed to faithfully represent causality and independence in concurrent systems, thereby exposing the concurrency underlying the computational content of classical proofs. The causal structure of concurrent strategies, paired with annotations by first-order terms, is used to specify the dependency between quantifiers implicit in proofs. Furthermore concurrent strategies can be composed, yielding a compositional proof of Herbrand's theorem, simply by interpreting classical sequent proofs in a well-chosen denotational model.
Cite as

Aurore Alcolei, Pierre Clairambault, Martin Hyland, and Glynn Winskel. The True Concurrency of Herbrand's Theorem. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{alcolei_et_al:LIPIcs.CSL.2018.5,
  author =	{Alcolei, Aurore and Clairambault, Pierre and Hyland, Martin and Winskel, Glynn},
  title =	{{The True Concurrency of Herbrand's Theorem}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{5:1--5:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.5},
  URN =		{urn:nbn:de:0030-drops-96723},
  doi =		{10.4230/LIPIcs.CSL.2018.5},
  annote =	{Keywords: Herbrand's theorem, Game semantics, True concurrency}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.16
Fully Abstract Models of the Probabilistic lambda-calculus

Authors: Pierre Clairambault and Hugo Paquet

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
We compare three models of the probabilistic lambda-calculus: the probabilistic Böhm trees of Leventis, the probabilistic concurrent games of Winskel et al., and the weighted relational model of Ehrhard et al. Probabilistic Böhm trees and probabilistic strategies are shown to be related by a precise correspondence theorem, in the spirit of existing work for the pure lambda-calculus. Using Leventis' theorem (probabilistic Böhm trees characterise observational equivalence), we derive a full abstraction result for the games model. Then, we relate probabilistic strategies to the weighted relational model, using an interpretation-preserving functor from the former to the latter. We obtain that the relational model is also fully abstract.
Cite as

Pierre Clairambault and Hugo Paquet. Fully Abstract Models of the Probabilistic lambda-calculus. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{clairambault_et_al:LIPIcs.CSL.2018.16,
  author =	{Clairambault, Pierre and Paquet, Hugo},
  title =	{{Fully Abstract Models of the Probabilistic lambda-calculus}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.16},
  URN =		{urn:nbn:de:0030-drops-96835},
  doi =		{10.4230/LIPIcs.CSL.2018.16},
  annote =	{Keywords: Game Semantics, Lambda-calculus, Probabilistic programming, Relational model, Full abstraction}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.81
Distributed Strategies Made Easy

Authors: Simon Castellan, Pierre Clairambault, and Glynn Winskel

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
Distributed/concurrent strategies have been introduced as special maps of event structures. As such they factor through their "rigid images," themselves strategies. By concentrating on such "rigid image" strategies we are able to give an elementary account of distributed strategies and their composition, resulting in a category of games and strategies. This is in contrast to the usual development where composition involves the pullback of event structures explicitly and results in a bicategory. It is shown how, in this simpler setting, to extend strategies to probabilistic strategies; and indicated how through probability we can track nondeterministic branching behaviour, that one might otherwise think lost irrevocably in restricting attention to "rigid image" strategies.
Cite as

Simon Castellan, Pierre Clairambault, and Glynn Winskel. Distributed Strategies Made Easy. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 81:1-81:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{castellan_et_al:LIPIcs.MFCS.2017.81,
  author =	{Castellan, Simon and Clairambault, Pierre and Winskel, Glynn},
  title =	{{Distributed Strategies Made Easy}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{81:1--81:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.81},
  URN =		{urn:nbn:de:0030-drops-81315},
  doi =		{10.4230/LIPIcs.MFCS.2017.81},
  annote =	{Keywords: Games, Strategies, Event Structures, Probability}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.12
Observably Deterministic Concurrent Strategies and Intensional Full Abstraction for Parallel-or

Authors: Simon Castellan, Pierre Clairambault, and Glynn Winskel

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
Although Plotkin’s parallel-or is inherently deterministic, it has a non-deterministic interpretation in games based on (prime) event structures - in which an event has a unique causal history - because they do not directly support disjunctive causality. General event structures can express disjunctive causality and have a more permissive notion of determinism, but do not support hiding. We show that (structures equivalent to) deterministic general event structures do support hiding, and construct a new category of games based on them with a deterministic interpretation of aPCFpor, an affine variant of PCF extended with parallel-or. We then exploit this deterministic interpretation to give a relaxed notion of determinism (observable determinism) on the plain event structures model. Putting this together with our previously introduced concurrent notions of well-bracketing and innocence, we obtain an intensionally fully abstract model of aPCFpor.
Cite as

Simon Castellan, Pierre Clairambault, and Glynn Winskel. Observably Deterministic Concurrent Strategies and Intensional Full Abstraction for Parallel-or. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{castellan_et_al:LIPIcs.FSCD.2017.12,
  author =	{Castellan, Simon and Clairambault, Pierre and Winskel, Glynn},
  title =	{{Observably Deterministic Concurrent Strategies and Intensional Full Abstraction for Parallel-or}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.12},
  URN =		{urn:nbn:de:0030-drops-77219},
  doi =		{10.4230/LIPIcs.FSCD.2017.12},
  annote =	{Keywords: Game semantics, parallel-or, concurrent games, event structures, full abstraction}
}
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